What is the period of the function $f(x)=-4\cos(5x-9)-7$ ? Give an exact value. units
Answer: Period in sinusoids of the form $y=a\cos(bx+c)+d$ Graphically, the period of a sinusoidal function is the horizontal distance between the ends of a single cycle of its graph. The period of a sinusoid of the form $y={a}\cos( bx + c) + {d}$ is equal to $\dfrac{2\pi}{| b|}$. [How can we justify this given our graphical understanding of period?] Finding the period The period of $f(x) = -4\cos({5}x-9)-7$ is: $\begin{aligned} \text{period}&=\dfrac{2\pi}{|{b}|}\\\\ &=\dfrac{2\pi}{| 5|} \\\\\\\\\\ &= \dfrac{2\pi}{5} \\ \end{aligned}$ The answer The period of $f(x) = -4\cos({5}x-9)-7$ is $\dfrac{2\pi}{5}$ units.